Question

What is the common difference of an AP in which a₂₇ – a₇ = 84? [CBSE 2017]

Answer 1

$$\begin{gathered} a_{27}=a+26d \\ {a}_7=a+6d \\ \mathrm{And} \\ {a}_{27}-a_7=84 \\ \Rightarrow a+26d-a-6d=84 \\ \Rightarrow 20d=84 \\ \Rightarrow d=\frac{21}{5}=4.2 \end{gathered}$$